HORIZON PHARMA, INC. WARRANT TO PURCHASE COMMON STOCK

Exhibit 4.1

HORIZON PHARMA, INC.

WARRANT TO PURCHASE COMMON STOCK

Warrant No.: 2012-[                    ]

Number of Shares of Common Stock: [                    ] (subject to adjustment)

Exercise Price: $4.57 per share (subject to adjustment) (“Exercise Price”)

Date of Issuance: September [    ], 2012 (“Issuance Date”)

Expiration Date: September [    ], 2017 (“Expiration Date”)

THIS CERTIFIES THAT, for value received, [                    ], or permitted assigns (the “Holder”), is entitled to subscribe for and purchase at the Exercise Price (defined above) from Horizon Pharma, Inc., a Delaware corporation, with its principal office at 520 Lake Cook Road, Suite 520, Deerfield, Illinois 60015 (the “Company”) up to [                    ] shares of the Common Stock of the Company (the “Common Stock”), subject to adjustment as provided herein.

1. DEFINITIONS. As used herein, the following terms shall have the following respective meanings:

(a) “Exercise Period” shall mean the period commencing on the Issuance Date and ending at 5:30 p.m., New York time, on the Expiration Date.

(b) “Exercise Shares” shall mean the shares of the Company’s Common Stock issued or issuable upon exercise of this Warrant, subject to adjustment pursuant to the terms herein, including but not limited to adjustment pursuant to Section 4 below.

(c) “Person” means an individual, a limited liability company, a partnership, a joint venture, a corporation, a trust, an unincorporated organization, any other entity and a government or any department or agency thereof.

(d) “Trading Day” means any day on which the Common Stock is traded on the The Nasdaq Global Market or The Nasdaq Capital Market, or, if such markets are not the principal trading market for the Common Stock, then on the principal securities exchange or securities market on which the Common Stock is then traded.

(e) “Warrant Agent” means Computershare Shareowner Services, LLC, with an address at 480 Washington Boulevard, Jersey City, New Jersey 07310, Attn: Cory McQuillen (or such successor Warrant Agent as the Company may designate by notice in writing to the Holder).

2. EXERCISE OF WARRANT.

2.1 Method of Exercise. The rights represented by this Warrant may be exercised in whole or in part at any time during the Exercise Period, by delivery of the following to the Company at its address set forth above (or at such other address as it may designate by notice in writing to the Holder):

(a) An executed Notice of Exercise in the form attached hereto; and

(b) Payment of the aggregate Exercise Price either (i) in cash or by check or wire transfer of immediately available funds, or (ii) pursuant to a cashless exercise, if available, as described below.

The conditions set forth in clauses (a) and (b) above are collectively referred to as the “Exercise Conditions”.

No ink-original Notice of Exercise shall be required, nor shall any medallion guarantee (or other type of guarantee or notarization) of any Notice of Exercise form be required. Notwithstanding anything herein to the contrary, the Holder shall not be required to physically surrender this Warrant to the Company until the Holder has purchased all of the Exercise Shares available hereunder and the Warrant has been exercised in full, in which case, the Holder shall surrender this Warrant to the Company for cancellation within three (3) Trading Days of the date the final Notice of Exercise is delivered to the Company. Partial exercises of this Warrant resulting in purchases of a portion of the total number of Exercise Shares

1

available hereunder shall have the effect of lowering the outstanding number of Exercise Shares purchasable hereunder in an amount equal to the applicable number of Exercise Shares purchased. The Holder and the Company shall maintain records showing the number of Exercise Shares purchased and the date of such purchases. The Holder and any assignee, by acceptance of this Warrant, acknowledge and agree that, by reason of the provisions of this paragraph, following the purchase of a portion of the Exercise Shares hereunder, the number of Exercise Shares available for purchase hereunder at any given time may be less than the amount stated on the face hereof.

2.2 Cashless Exercise. Notwithstanding any provisions herein to the contrary, if, at the time this Warrant is exercised, (a) there is no effective registration statement registering, or the prospectus contained therein is not available for, the issuance of the Exercise Shares to the Holder, (ii) all of the Exercise Shares are not then registered for resale by the Holder into the market at market prices from time to time on an effective registration statement for use on a continuous basis (or the prospectus contained therein is not available for use) and (iii) the Current Market Price (as defined below) of one share of Common Stock is greater than the Exercise Price (at the date of calculation as set forth below), then in lieu of exercising this Warrant by payment of cash, the Holder may exercise this Warrant by a cashless exercise by surrender of this Warrant at the principal office of the Company (or at such other address as it may designate by notice in writing to the Holder) together with the properly endorsed Notice of Exercise and the Company shall issue to the Holder a number of shares of Common Stock computed using the following formula:

“Current Market Price” means on any particular date:

(a) if the Common Stock is traded on The Nasdaq Global Market or The Nasdaq Capital Market, the closing price of the Common Stock of the Company on such market on the Trading Day prior to the applicable date of valuation;

(b) if the Common Stock is traded on any registered national stock exchange but is not traded on The Nasdaq Global Market or The Nasdaq Capital Market, the closing price of the Common Stock of the Company on such exchange on the Trading Day prior to the applicable date of valuation;

(c) if the Common Stock is traded over-the-counter, but not on The Nasdaq Global Market, The Nasdaq Capital Market or a registered national stock exchange, the closing bid price of the Common Stock of the Company on the day prior to the applicable date of valuation; and

(d) if there is no active public market for the Common Stock, the value thereof, as determined in good faith by the Board of Directors of the Company upon due consideration of the proposed determination thereof by the Holder.

2.3 Exercise Limitation. Anything to the contrary in this Warrant notwithstanding, the Company shall not effect the exercise of this Warrant, and the Holder shall not have the right to exercise this Warrant, to the extent that after giving effect to such exercise, such Holder (together with such Holder’s affiliates and any other Persons acting as a group together) would beneficially own in excess of 4.99% (the “Maximum Percentage”) of the shares of Common Stock outstanding immediately after giving effect to such exercise. For purposes of the foregoing sentence, the aggregate number of

2

shares of Common Stock beneficially owned by such Person and its affiliates shall include the number of shares of Common Stock issuable upon exercise of this Warrant with respect to which the determination of such sentence is being made, but shall exclude shares of Common Stock which would be issuable upon (i) exercise of the remaining, unexercised portion of this Warrant beneficially owned by such Person and its affiliates and (ii) exercise or conversion of the unexercised or unconverted portion of any other securities of the Company beneficially owned by such Person and its affiliates (including, without limitation, any convertible notes or convertible preferred stock or warrants) subject to a limitation on conversion or exercise analogous to the limitation contained herein. Except as set forth in the preceding sentence, for purposes of this paragraph, beneficial ownership shall be calculated in accordance with Section 13(d) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), it being acknowledged that the Company is not representing to the Holder that such calculation is in compliance with Section 13(d) of the Exchange Act, and the Holder is solely responsible for any schedules required to be filed in accordance therewith. For purposes of this Warrant, in determining the number of outstanding shares of Common Stock, the Holder may rely on the number of outstanding shares of Common Stock as reflected in (1) the Company’s most recent Form 10-K, Proxy Statement, Form 10-Q, Current Report on Form 8-K or other public filing with the Securities and Exchange Commission, as the case may be, (2) a more recent public announcement by the Company or (3) any other notice by the Company or the Transfer Agent setting forth the number of shares of Common Stock outstanding. For any reason at any time, upon the written or oral request of the Holder, where such request indicates that it is being made pursuant to this Warrant, the Company shall within two Trading Days confirm orally and in writing to the Holder the number of shares of Common Stock then outstanding. In any case, the number of outstanding shares of Common Stock shall be determined after giving effect to the conversion or exercise of securities of the Company, including the Warrants, by the Holder and its affiliates since the date as of which such number of outstanding shares of Common Stock was reported. By written notice to the Company, the Holder may increase or decrease the Maximum Percentage to any other percentage not in excess of 9.99% specified in such notice; provided, that (i) any such increase will not be effective until the 61^st day after such notice is delivered to the Company and (ii) any such increase or decrease will apply only to the particular Holder delivering the notice and not to any subsequent holder of this Warrant.

2.4 [Reserved]

2.5 No Settlement for Cash. Except as provided in Section 4.3, this Warrant cannot be settled with the Company for cash.

2.6 Delivery of Shares. Exercise Shares acquired hereunder shall be delivered to the Holder within three Trading Days after the date on which this Warrant shall have been validly exercised pursuant to the Exercise Conditions. On or before the first Trading Day following the date on which the Exercise Notice is delivered, the Company shall transmit by email or facsimile an acknowledgment of confirmation of receipt of the Exercise Notice and the aggregate Exercise Price (if applicable) to the Holder and the Company’s transfer agent for the Common Stock (the “Transfer Agent”). The Company shall deliver any objection to the proper satisfaction of the Exercise Conditions on or before the first Trading Day following the date on which the Company has received the Exercise Notice. In the event of any discrepancy or dispute, the records of the Company shall be controlling and determinative in the absence of manifest error. On or before the third Trading Day following the date on which the Exercise Conditions have been satisfied (the “Share Delivery Date”), the Company shall, upon the request of the Holder, credit such aggregate number of shares of Common Stock to which the Holder is entitled pursuant to such exercise to the Holder’s or its designee’s balance account with The Depository Trust Company (“DTC”) through its Deposit Withdrawal Agent Commission system, or if the Transfer Agent is not participating in the Fast Automated Securities Transfer Program (the “FAST Program”) or if the certificates are required to bear a legend regarding restriction on transferability, issue and dispatch by overnight courier to the address as specified in the Exercise Notice, a certificate, registered in the Company’s share register in the name of the Holder or its designee, for the number of shares of Common Stock to which the Holder is entitled pursuant to such exercise. Upon satisfaction of the Exercise Conditions and surrender of this Warrant (if required), the Holder shall be deemed for all corporate purposes to have become the holder of record of the Exercise Shares with respect to which this Warrant has been exercised, irrespective of the date such Exercise Shares are credited to the Holder’s DTC account or the date of delivery of the certificates evidencing such Exercise Shares, as the case may be.

2.7 Failure to Deliver Exercise Shares. If the Company fails to cause the Transfer Agent to transmit to the Holder the Exercise Shares pursuant to Section 2.6 by the end of the Share Delivery Date, then the Holder will have the right to rescind such exercise prior to the delivery of the Exercise Shares. If the Company fails to deliver to the Holder Exercise Shares pursuant to Section 2.6 by the end of the Share Delivery Date, and the Holder or the Holder’s brokerage firm

3

thereafter (but before delivery of the Exercise Shares) purchases shares of the same class and series as the Exercise Shares to deliver in satisfaction of a sale by the Holder of the Exercise Shares which the Holder anticipated receiving upon such exercise (a “Buy-In”), the Company shall (A) pay in cash to the Holder the amount by which,

(i) the Holder’s total purchase price (including brokerage commissions, if any) for the shares so purchased, exceeds

(ii) the amount obtained by multiplying (1) the number of Exercise Shares that the Company was required to deliver to the Holder in connection with the exercise, by (2) the price at which the sell order giving rise to such purchase obligation was executed, and

(B) at the option of the Holder, either reinstate the portion of the Warrant and equivalent number of Exercise Shares for which such exercise was not honored (in which case such exercise shall be deemed rescinded) or deliver to the Holder the number of shares of Common Stock that would have been issued had the Company timely complied with its exercise and delivery obligations hereunder.

The Holder shall provide the Company prompt written notice indicating the amounts payable to the Holder in respect of any Buy-In, together with applicable confirmations and other evidence reasonably requested by the Company (a “Buy-In Notice”). The Company shall pay the amounts payable to the Holder in respect of any Buy-In within three Trading Days after the Company’s receipt of the Buy-In Notice.

3. COVENANTS OF THE COMPANY.

3.1 Covenants as to Exercise Shares. The Company covenants and agrees that it will at all times during the Exercise Period, have authorized and reserved, free from preemptive rights, a sufficient number of shares of its Common Stock to provide for the exercise of the rights represented by this Warrant. All Exercise Shares will, upon issuance, be validly issued and outstanding, fully paid and nonassessable, and free from all taxes, liens and charges with respect to the issuance thereof. If at any time during the Exercise Period the number of authorized but unissued shares of Common Stock shall not be sufficient to permit exercise of this Warrant, the Company will take such corporate action as may, in the opinion of its counsel, be necessary to increase its authorized but unissued shares of Common Stock (or other securities as provided herein) to such number of shares as shall be sufficient for such purposes.

3.2 No Impairment. Except and to the extent as waived or consented to by the Holder, the Company will not, by amendment of its Certificate of Incorporation (as such may be amended from time to time), or through any means, avoid or seek to avoid the observance or performance of any of the terms to be observed or performed hereunder by the Company, but will at all times in good faith assist in the carrying out of all the provisions of this Warrant and in the taking of all such action as may be necessary or appropriate in order to protect the exercise rights of the Holder against impairment.

4. CERTAIN ADJUSTMENTS.

4.1 Subdivisions, Combinations and Other Issuances. In the event the Company pays a dividend in Common Stock or makes a distribution in Common Stock or any other equity or equity equivalent securities payable in shares of Common Stock to holders of its outstanding Common Stock; subdivides its outstanding Common Stock into a greater number of shares; combines its outstanding Common Stock into a smaller number of shares; or issues any shares of its capital stock in a reclassification of the Common Stock, the number and class of shares available under this Warrant in the aggregate and the Exercise Price shall be correspondingly adjusted to give the Holder of this Warrant, on exercise for the same aggregate Exercise Price, the total number, class, and kind of shares as the Holder would have owned had this Warrant been exercised prior to the event and had the Holder continued to hold such shares until after the event requiring adjustment. The form of this Warrant need not be changed because of any adjustment in the number, class, and kind of shares subject to this Warrant. Upon request, the Company shall promptly provide to the Holder a certificate from its Chief Financial Officer, which certificate shall specify the Exercise Price and number, class and kind of shares under this Warrant after giving effect to such adjustment.

4.2 Pro Rata Distributions. If the Company, at any time while this Warrant is outstanding, distributes to holders of Common Stock (i) evidences of its indebtedness, (ii) any security (other than a distribution of Common Stock

4

subject to Section 4.1), (iii) rights or warrants to subscribe for or purchase any security, or (iv) any other asset (in each case, “Distributed Property”), then in each such case the Holder shall be entitled upon exercise of this Warrant for the purchase of any or all of the Exercise Shares, to receive the amount of Distributed Property which would have been payable to the Holder had such Holder been the holder of such Exercise Shares on the record date for the determination of stockholders entitled to such Distributed Property. The Company will at all times set aside and keep available for distribution to the Holder upon exercise of this Warrant a portion of the Distributed Property to satisfy the distribution to which such Holder is entitled pursuant to the preceding sentence.

4.3 Fundamental Transactions. If the Company consummates (i) a merger or consolidation with or into another entity, as a result of which the holders of the Company’s outstanding voting securities as of immediately prior to such merger or consolidation hold less than a majority of the outstanding voting securities of the surviving or successor entity as of immediately after such merger or consolidation or (ii) a sale, transfer or other disposition of all or substantially all its property, assets or business to another person or entity (any such transaction being hereinafter referred to as a “Fundamental Transaction”), then the Company shall ensure that lawful and adequate provision shall be made whereby the Holder shall thereafter have the right to purchase and receive upon the basis and upon the terms and conditions herein specified and in lieu of the Exercise Shares immediately theretofore issuable upon exercise of this Warrant, such shares of stock, securities or assets as would have been issuable or payable with respect to or in exchange for a number of Exercise Shares equal to the number of Exercise Shares immediately theretofore issuable upon exercise of this Warrant, had such Fundamental Transaction not taken place. The provisions of this Section 4.3 shall similarly apply to successive consolidations, mergers, sales, transfers or other dispositions.

5. FRACTIONAL SHARES. No fractional shares shall be issued upon the exercise of this Warrant as a consequence of any adjustment pursuant hereto. All Exercise Shares (including fractions) issuable upon exercise of this Warrant may be aggregated for purposes of determining whether the exercise would result in the issuance of any fractional share. If, after aggregation, the exercise would result in the issuance of a fractional share, the Company shall, in lieu of issuance of any fractional share, pay the Holder otherwise entitled to such fraction a sum in cash equal to the product resulting from multiplying the then Current Market Price of an Exercise Share by such fraction.

6. NO STOCKHOLDER RIGHTS. This Warrant in and of itself shall not entitle the Holder to any voting rights or other rights as a stockholder of the Company.

7. REGISTRATION, TRANSFER AND REISSUANCE.

7.1 Registration. The Company or the Warrant Agent shall register this Warrant, upon the records to be maintained by the Company or the Warrant Agent for that purpose (the “Warrant Register”), in the name of the record Holder hereof from time to time. The Company and the Warrant Agent may deem and treat the registered Holder of this Warrant as the absolute owner hereof for the purpose of any exercise hereof or any distribution to the Holder, and for all other purposes, absent actual notice to the contrary. The Company or the Warrant Agent shall also register any transfer, exchange, reissuance or cancellation of any portion of this Warrant in the Warrant Register.

7.2 Transfer. This Warrant may be offered for sale, sold, transferred or assigned without the consent of the Company, except as may otherwise be required by applicable securities laws. Subject to applicable securities laws, if this Warrant is to be transferred, the Holder shall surrender this Warrant to the Warrant Agent, together with all applicable transfer taxes, whereupon the Company will cause the Warrant Agent to, forthwith issue and deliver upon the order of the Holder a new Warrant (in accordance with Section 7.4), registered as the Holder may request, representing the right to purchase the number of Exercise Shares being transferred by the Holder and, if less then the total number of Exercise Shares then underlying this Warrant is being transferred, a new Warrant (in accordance with Section 7.4) to the Holder representing the right to purchase the number of Exercise Shares not being transferred. The acceptance of the new Warrant by the transferee thereof shall be deemed the acceptance by such transferee of all of the rights and obligations in respect of the new Warrant that the Holder has in respect of this Warrant.

7.3 Lost, Stolen, Mutilated or Destroyed Warrant. If this Warrant is lost, stolen, mutilated or destroyed, the Company may, on such terms as to indemnity or otherwise as it may reasonably impose (which shall, in the case of a mutilated Warrant, include the surrender thereof to the Warrant Agent), cause the Warrant Agent to issue a new Warrant of like denomination and tenor as the Warrant so lost, stolen, mutilated or destroyed.

5

7.4 Issuance of New Warrants. Whenever the Company or the Warrant Agent, as directed by the Company, is required to issue a new Warrant pursuant to the terms of this Warrant, such new Warrant shall (a) be of like tenor with this Warrant, (b) represent, as indicated on the face of such new Warrant, the right to purchase the Exercise Shares then underlying this Warrant (or in the case of a new Warrant being issued pursuant to Section 7.2 or Section 7.3, the Exercise Shares designated by the Holder which, when added to the number of shares of Common Stock underlying the other new Warrants issued in connection with such issuance, does not exceed the number of Exercise Shares then underlying this Warrant), (c) have an issuance date, as indicated on the face of such new Warrant which is the same as the Issuance Date and (d) have the same rights and conditions as this Warrant.

8. MODIFICATIONS AND WAIVER. This Warrant and any provision hereof may be waived, modified or amended only by an instrument in writing signed by the Company and the Holder.

9. NOTICES, ETC. All notices required or permitted hereunder shall be in writing and shall be deemed effectively given: (a) upon personal delivery to the party to be notified, (b) when sent by confirmed email, telex or facsimile if sent during normal business hours of the recipient, if not, then on the next business day, (c) five days after having been sent by registered or certified mail, return receipt requested, postage prepaid, or (d) one business day after deposit with a nationally recognized overnight courier, specifying next day delivery, with written verification of receipt. All communications shall be sent to the Company at the address listed on the signature page and to the Holders at the addresses on the Company records, or at such other address as the Company or Holder may designate by ten days’ advance written notice to the other party hereto.

10. ACCEPTANCE. Receipt of this Warrant by the Holder shall constitute acceptance of and agreement to all of the terms and conditions contained herein.

11. GOVERNING LAW. This Warrant and all rights, obligations and liabilities hereunder shall be governed by the laws of the State of New York without regard to the principles of conflict of laws.

12. DESCRIPTIVE HEADINGS. The descriptive headings of the several paragraphs of this Warrant are inserted for convenience only and do not constitute a part of this Warrant. The language in this Warrant shall be construed as to its fair meaning without regard to which party drafted this Warrant.

13. SEVERABILITY. The invalidity or unenforceability of any provision of this Warrant in any jurisdiction shall not affect the validity or enforceability of such provision in any other jurisdiction, or affect any other provision of this Warrant, which shall remain in full force and effect.

14. ENTIRE AGREEMENT. This Warrant constitutes the entire agreement between the parties pertaining to the subject matter contained in it and supersedes all prior and contemporaneous agreements, representations, and undertakings of the parties, whether oral or written, with respect to such subject matter.

[Signature Page Follows]

6

IN WITNESS WHEREOF, the Company has caused this Warrant to be executed by its duly authorized officer.

NOTICE OF EXERCISE

TO: HORIZON PHARMA, INC.

1. The undersigned hereby elects to purchase                      Exercise Shares of the Company pursuant to the terms of the attached Warrant (only if exercised in full), and tenders herewith payment of the aggregate Exercise Price in full, together with all applicable transfer taxes, if any.

2. Payment shall take the form of (check applicable box):

3. Please issue a certificate or certificates representing said Exercise Shares in the name of the undersigned or in such other name as is specified below:

The Exercise Shares shall be delivered to the following DWAC Account Number or by physical delivery of a certificate to:

4. By its delivery of this Exercise Notice, the undersigned represents and warrants to the Company that in giving effect to the exercise evidenced hereby the Holder will not beneficially own in excess of the number of shares of Common Stock (determined in accordance with Section 13(d) of the Securities Exchange Act of 1934, as amended) permitted to be owned under Section 2.3 of the Warrant to which this notice relates.

DATED:                     

ASSIGNMENT FORM

(To assign the foregoing Warrant execute this form and supply required information. Do not use this form to purchase shares.)

FOR VALUE RECEIVED, the foregoing Warrant and all rights evidenced thereby are hereby assigned to

Name:

(Please Print)

Address:

(Please Print)

Dated:             , 201     

Holder’s

Signature:                                                                          

Holder’s

Address:                                                                              

NOTE: The signature to this Assignment Form must correspond with the name as it appears on the face of the Warrant, without alteration or enlargement or any change whatever. Officers of corporations and those acting in a fiduciary or other representative capacity should file proper evidence of authority to assign the foregoing Warrant.